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GRE Practice Test

GRE Practice: Comparison GRE Practice Test 5


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1. Question:

There are three events A, B and C, one of which must happen and at a time, only one can happen. The odds are 8 to 3 against A, 5 to 2 against B.

Column A Column B
Probability of occurrence of C Probability of occurrence of A
  1. Quantity A is greater
  2. Quantity B is greater
  3. The quantities are equal
  4. The relationship cannot be determined from the information given

Correct Answer: A

Explanation:

Probability of occurrence of A, P(A)=3/(8+3) = 3/11
Probability of occurrence of B, P(B)=2/(5+2) = 2/7
Since one and only one event can occur at a time, we have
P(A)+P(B)+P(C)=1
3/11+2/7+P(C)=1
P(C)=1-2/7-3/11
=(77-22-21)/77
=34/77
P(A)=3/11 and P(C)=34/77
P(A)<P(C)
Option A is correct.

2. Question:

Column A Column B
Distance travelled by the tip of a minutes' needle in 35 minutes Distance travelled by Rob in 35 minutes at the speed of 5 km/hr
  1. Quantity A is greater
  2. Quantity B is greater
  3. The quantities are equal
  4. The relationship cannot be determined from the information given

Correct Answer: D

Explanation:

We cannot calculate the distance travelled by the minutes' needle since we do not know the length of the needle.
Hence, the comparison cannot be made.
Option D is correct.

3. Question:

A child runs along the four sides of a square playground at speeds 200, 300, 600 and 800 m/hr.

Column A Column B
Average speed of the child around the playground m/hr 384 m/hr
  1. Quantity A is greater
  2. Quantity B is greater
  3. The quantities are equal
  4. The relationship cannot be determined from the information given

Correct Answer: B

Explanation:

Let each side of the square be a km.
Speed = Distance/time
Time = a/200+a/300+a/600+a/800
= a/100(1/2+1/3+1/6+1/8)
= a/100*(12+8+4+3)/24
= a/100*27/24
= 9a/800
Average speed = Total distance/time
= 4a/9a/800
= 4*800/9
= 355.55 m/hr
Option B is correct.

4. Question:

P(x,-1) is the centroid of the triangle ABC with vertices A(3,-5), B(-7,2x) and C(5x,-2).

Column A Column B
PA PC
  1. Quantity A is greater
  2. Quantity B is greater
  3. The quantities are equal
  4. The relationship cannot be determined from the information given

Correct Answer: B

Explanation:

Since (x,-1) is the centroid of the triangle, we have
x = (3-7+5x)/3 and -1=(-5+2x-2)/3
3x=-4+5x and -3 = -7+2x
5x-3x=4 and -3+7=2x
2x=4 and 4=2x
x=2

P(2,-1), A(3,-5) and C(10,-2)
PA=Sqrt[(3-2)^2+(-5+1)^2] and PC=Sqrt[(10-2)^2+(-2+1)^2]
PA=Sqrt(1+16) and PC=Sqrt(64+1)
PA=Sqrt(17) and PC=Sqrt(65)
Option B is correct.

5. Question:

Column A Column B
Revolutions made by a wheel of diameter 35 cm to cover a distance of 11 km Revolutions made by a wheel of diameter 11cm to cover a distance of 35 km
  1. Quantity A is greater
  2. Quantity B is greater
  3. The quantities are equal
  4. The relationship cannot be determined from the information given

Correct Answer: B

Explanation:

The wheel with smaller diameter will require more revolutions to cover the same distance as covered by a wheel with greater diameter.
The wheel with diameter 35 cm will take lesser revolutions than the wheel with diameter 11 cm to cover the same distance.
The distance covered by the smaller wheel is greater and hence it makes more revolutions to cover the distance required.
Option B is correct.

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